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Cellular fluidics

The natural world provides many examples of multiphase transport and reaction processes that have been optimized by evolution. These phenomena take place at multiple length and time scales and typically include gas–liquid–solid interfaces and capillary phenomena in porous media. Many biological and living systems have evolved to optimize fluidic transport. However, living things are exceptionally complex and very difficult to replicate, and human-made microfluidic devices (which are typically planar and enclosed) are highly limited for multiphase process engineering. In this paper, we introduce the concept of cellular fluidics: a platform of unit-cell-based, three-dimensional structures—enabled by emerging 3D printing methods—for the deterministic control of multiphase flow, transport and reaction processes. We show that flow in these structures can be ‘programmed’ through architected design of cell type, size and relative density. We demonstrate gas–liquid transport processes such as transpiration and absorption, using evaporative cooling and CO 2 capture as examples. We design and demonstrate preferential liquid and gas transport pathways in three-dimensional cellular fluidic devices with capillary-driven and actively pumped liquid flow, and present examples of selective metallization of pre-programmed patterns. Our results show that the design and fabrication of architected cellular materials, coupled with analytical and numerical predictions of steady-state and dynamic behaviour of multiphase interfaces, provide deterministic control of fluidic transport in three dimensions. Cellular fluidics may transform the design space for spatial and temporal control of multiphase transport and reaction processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

A method of depositing a multiphase material. The method includes providing a Continuous Multifunctional Composite (CMC) phase containing at least one continuous element in a polymeric matrix, passing the CMC phase through a feeding system containing a cutting system, producing a predetermined length of the CMC phase, providing a flow a molten polymer such that the molten polymer and the CMC phase are merged into a continuous co-extrusion nozzle so as to produce a co-extruded multiphase material, and depositing the co-extruded multiphase material onto a surface. An apparatus for depositing a multiphase material. The apparatus contains a co-extrusion nozzle, a means to introduce a CMC phase and a molten polymer into the co-extrusion nozzle, such that the molten polymer and the CMC phase are co-extruded and deposited on a surface. An article containing a CMC phase containing continuous elements embedded in a polymer resin forming a multiphase structure.

Barocio, Eduardo↗

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

A method of depositing a multiphase material. The method includes providing a Continuous Multifunctional Composite (CMC) phase containing at least one continuous element in a polymeric matrix, passing the CMC phase through a feeding system containing a cutting system, producing a predetermined length of the CMC phase, providing a flow a molten polymer such that the molten polymer and the CMC phase are merged into a continuous co-extrusion nozzle so as to produce a co-extruded multiphase material, and depositing the co-extruded multiphase material onto a surface. An apparatus for depositing a multiphase material. The apparatus contains a co-extrusion nozzle, a means to introduce a CMC phase and a molten polymer into the co-extrusion nozzle, such that the molten polymer and the CMC phase are co-extruded and deposited on a surface. An article containing a CMC phase containing continuous elements embedded in a polymer resin forming a multiphase structure.

Barocio, Eduardo↗

Methods and apparatus for additive manufacturing utilizing multifunctional composite materials, and articles made therefrom

A method of depositing a multiphase material. The method includes providing a Continuous Multifunctional Composite (CMC) phase containing at least one continuous element in a polymeric matrix, passing the CMC phase through a feeding system containing a cutting system, producing a predetermined length of the CMC phase, providing a flow a molten polymer such that the molten polymer and the CMC phase are merged into a continuous co-extrusion nozzle so as to produce a co-extruded multiphase material, and depositing the co-extruded multiphase material onto a surface. An apparatus for depositing a multiphase material. The apparatus contains a co-extrusion nozzle, a means to introduce a CMC phase and a molten polymer into the co-extrusion nozzle, such that the molten polymer and the CMC phase are co-extruded and deposited on a surface. An article containing a CMC phase containing continuous elements embedded in a polymer resin forming a multiphase structure.

Barocio, Eduardo↗

Verification of the Two-Fluid Model in the Spectral Element Code Nek-2P for Adiabatic Flow Conditions

The simulation of multiphase flow is a difficult physical, computational, and numerical problem. Sophisticated tools are necessary to provide results encompassing a wide range of physical phenomena. The development of these tools must be supported by rigorous analysis and ongoing efforts of verification and validation to ensure the accuracy of simulations. The Nek-2P multiphase code is being developed at Argonne with the general goal of simulating a wide range of multiphase flows and the primary goal of simulating boiling flows in LWR fuel assemblies. As part of this, there is an ongoing effort to verify the code and validate the underlying physical models. The objective of this work is to present recent results in the verification of Nek-2P. As a starting point, this work is focused on adiabatic flows for the sake of simplicity with the immediate next planned step to expand the effort to include heat and mass transfer. Details of the verification of the implemented mass fraction transport, momentum conservation, and pressure equations in Nek-2P are presented. Results of simulations are compared to analytic solutions when possible, however due to the complexity of multiphase flows, these are seldom available. To overcome this difficulty, an independent model is used to provide solutions for comparison.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The role of the spatial heterogeneity and correlation length of surface wettability on two-phase flow in a CO 2 -water-rock system

This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.

58 GEOSCIENCES↗

A consistent and conservative model and its scheme for N -phase- M -component incompressible flows

Here, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Kinetic Model of the Long-Term Corrosion of Glass-Ceramic Materials

Multiphase waste forms show promise for increased waste loading and for the ability to dispose of contaminated solid and particulate waste through direct densification. However, achieving predictive capability for long-term durability of multiphase waste forms, and thus assessing their possible deployment, requires expanding the current, limited knowledge base. Here, we describe the development of a corrosion model of a two-phase waste form consisting of crystals of known volume fraction embedded in a glass matrix. This model accounts for the dissolution of both the crystalline and glass phases as well as the hydration of the glass phase through an ion exchange reaction. Because of the large difference in solubility between the two phases, the reactive surface of the crystalline phase is a function of the extent of dissolution of the glass phase in this model. Model parameterization was performed using corrosion data, such as from single-pass flow-through tests, for the individual phases. The parameterized corrosion model was evaluated against static dissolution test data for a glass-ceramic multiphase waste form. This evaluation demonstrated the model’s ability to reproduce the time-dependent release of key tracers of glass and crystalline phase dissolution. Hence, the development of a kinetic model provides a pathway for long-term durability predictions and thus the use of multiphase waste forms in nuclear cleanup missions.

Kerisit, Sebastien N.↗

Texture Development and Stress–Strain Partitioning in Periclase + Halite Aggregates

Multiphase materials are widely applied in engineering due to desirable mechanical properties and are of interest to geoscience as rocks are multiphase. High-pressure mechanical behavior is important for understanding the deep Earth where rocks deform at extreme pressure and temperature. In order to systematically study the underlying physics of multiphase deformation at high pressure, we perform diamond anvil cell deformation experiments on MgO + NaCl aggregates with varying phase proportions. Lattice strain and texture evolution are recorded using in-situ synchrotron x-ray diffraction and are modeled using two-phase elasto-viscoplastic self-consistent (EVPSC) simulations to deduce stress, strain, and deformation mechanisms in individual phases and the aggregate. Texture development of MgO and NaCl are affected by phase proportions. In NaCl, a (100) compression texture is observed when small amounts of MgO are present. In contrast, when deformed as a single phase or when large amounts of MgO are present, NaCl develops a (110) texture. Stress and strain evolution in MgO and NaCl also show different trends with varying phase proportions. Based on the results from this study, we construct a general scheme of stress evolution as a function of phase proportion for individual phases and the aggregate.

Lin, Feng↗

Quaternary borocarbides: New class of intermetallic superconductors

Our recent discovery of superconductivity (SC) in the four-element multiphase Y-Ni-B-C system at an elevated temperature (TC approximately 12 K) has opened up great possibilities of identifying new superconducting materials and generating new physics. Superconductivity with Tc (greater than 20 K) higher than that known so far in bulk intermetallics has been observed in multiphase Y-Pd-B-C and Th-Pd-B-C systems and a family of single phase materials RENi2B2C (RE= Y, rare earth) have been found. Our investigations show YNi2B2C to be a strong coupling hard type-II SC. HC2(T) exhibits an unconventional temperature dependence. Specific heat and magnetization studies reveal coexistence of SC and magnetism in RNi2B2C (R = Ho, Er, Tm) with magnetic ordering temperatures (Tc approximately 8 K, 10.5 K, 11 K and Tm approximately 5 K, approximately 7K, approximately 4 K respectively) that are remarkably higher than those in known magnetic superconductors . Mu-SR studies suggest the possibility of Ni atoms carrying a moment in TmNi2B2C. Resistivity results suggests a double re-entrant transition (SC-normal-SC) in HoNi2B2C. RENi2B2C (RE = Ce, Nd, Gd) do not show SC down to 4.2 K. The Nd- and Gd-compounds order magnetically at approximately 4.5 K and approximately 19.5 K, respectively. Two SC transitions are observed in Y-Pd-B-C (Tc approximately 22 K, approximately 10 K) and in Th-Pd-B-C (Tc approximately 20 K, approximately 14 K) systems, which indicate that there are at least two structures which support SC in these borocarbides. In our multiphase ThNi2B2C we observe SC at approximately 6 K. No SC was seen in multiphase UNi2B2C, UPd2B2C, UOs2Ge2C and UPd5B3C(0.35) down to 4.2 K. Tc in YNi2B2C is depressed by substitutions (Gd, Th and U at Y-sites and Fe, Co at Ni-sites).

Nagarajan, R.↗

Critical Load Exceedances for North America and Europe using an Ensemble of Models and an Investigation of Causes for Environmental Impact Estimate Variability: An AQMEII4 Study

Exceedances of critical loads for deposition of sulphur (S) and nitrogen (N) to different ecosystems were estimated using European and North American ensembles of air quality models, under Phase 4 of the Air Quality Model Evaluation International Initiative (AQMEII4), to identify where risk of ecosystem harm is expected to occur based on model deposition estimates. The ensembles were driven by common emissions and lateral boundary condition inputs. Model output was regridded to common North American and Europe 0.125° resolution domains, which were then used to calculate critical load exceedances. New, targeted deposition diagnostics implemented in AQMEII4 allowed an unprecedented level of post-simulation analysis to be carried out and facilitated the identification of specific causes of model-to-model variability in critical load exceedance estimates. New datasets for North American critical loads for acidity for forest soil water and aquatic ecosystems were combined with the ensemble deposition predictions to show a substantial decrease in the area and number of locations in exceedance between 2010 and 2016 (forest soils: 13.2 % to 6.1 %; aquatic ecosystems: 21.2 % to 11.4 %). All models agreed in the direction of the ensemble exceedance change between 2010 and 2016. The North American ensemble also predicted a decrease in both severity and total area in exceedance between the years 2010 and 2016 for eutrophication-impacted ecosystems in the USA (sensitive epiphytic lichen: 81.5 % to 75.8 %). The exceedances for herbaceous community richness also decreased between 2010 and 2016, from 13.9 % to 3.9 %. The uncertainty associated with the North American eutrophication results is high; there were sharp differences between the models in both predictions of total N deposition and the change in N deposition, and hence in the predicted eutrophication exceedances between the two years. The European ensemble was used to predict relatively static exceedances of critical loads with respect to acidification (4.48 % to 4.32 % from 2009 to 2010) while eutrophication exceedance increased slightly (60.2 % to 62.2 %). While most models showed the same changes in critical load exceedances as the ensemble between the two years, the spatial extent and magnitude of exceedances varied significantly between the models. The reasons for this variation were examined in detail by first ranking the relative contribution of different sources of sulphur and nitrogen deposition in terms of deposited mass and model-to-model variability in that deposited mass, followed by their analysis using AQMEII4 diagnostics, along with evaluation of the most recent literature. All models in both the North American and European ensembles had net annual negative biases with respect to observed wet deposition of sulphate, nitrate and ammonium. Diagnostics and recent literature suggest that this bias may stem from insufficient cloud scavenging of aerosols and gases, and may be improved through the incorporation of multiphase hydrometeor scavenging within the modelling frameworks. The inability of North American models to predict the timing of the seasonal peak in wet ammonium ion deposition (observed maximum was in April, while all models predicted a June maximum) may also relate to the need for multiphase hydrometeor scavenging (absence of snow scavenging in all models employed here). High variability in the relative importance of particulate sulphate, nitrate and ammonium deposition fluxes between models was linked to the use of updated particle dry deposition parameterizations in some models. However, recent literature and further development of some of the models within the ensemble suggests these particulate biases may also be ameliorated via the incorporation of multiphase hydrometeor scavenging. Annual sulphur and nitrogen deposition prediction variability was linked to SO 2 and HNO 3 dry deposition parameterizations, and diagnostic analysis showed that the cuticle and soil deposition pathways dominate the deposition mass flux of these species. Further work improving parameterizations for these deposition pathways should reduce variability in model acidifying gas deposition estimates. The absence of base cation chemistry in some models was shown to be a major factor in positive biases in fine mode particulate ammonium and particle nitrate concentrations. Models employing ammonia bidirectional fluxes had both the largest and the smallest magnitude biases, depending on the model and bidirectional flux algorithm employed. A careful analysis of bidirectional flux models suggests that those with poor NH 3 performance may underestimate the extent of NH 3 emissions fluxes from forested areas. Based on these results, an increased process-research focus is therefore recommended for the following model processes and on observations which may assist in model evaluation and improvement: multiphase hydrometeor scavenging combined with updated particle dry deposition, cuticle and soil deposition pathway algorithms for acidifying gases, base cation chemistry and emissions, and NH 3 bidirectional fluxes. Comparisons with satellite observations suggest that oceanic NH 3 emissions sources should be included in regional chemical transport models. The choice of land use database employed within any given model was shown to significantly influence deposition totals in several instances, and employing a common land use database across chemical transport models and critical load calculations is recommended for future work.

critical loads↗

Multi-phase AC/AC step-down converter for distribution systems

A step-down AC/AC converter for use in an electric distribution system includes at least one chopper circuit for each one of a plurality of phases of the AC power, each chopper circuit including a four-quadrant switch coupled in series between primary and secondary sides of the chopper circuit and a current-bidirectional two-quadrant switch coupled between the secondary side of the chopper circuit and a common node. Each current-bidirectional two-quadrant switch is oriented in the same direction, with respect to the secondary side of the corresponding chopper circuit and the common node. The converter further includes a control circuit configured to pulse-width-modulate control inputs of the switches, to convert a first multiphase AC voltage at the primary sides of the chopper circuits to a second multiphase AC voltage at the secondary sides of the chopper circuits, the second multiphase AC voltage being lower in voltage than the first multiphase AC voltage.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A scalable compressible volume of fluid solver using a stratified flow model

Here, in this paper, a Volume of Fluid method which uses a Stratified Flow model for flux calculation is proposed to solve a compressible multiphase flow in a way that has high parallel efficiency. The solver is part of an open-source computing tool to study fuel entrainment and combustion in the application of paraffin-based hybrid rocket motors. This paper focuses on the compressible Volume of Fluid solver for the liquid and gaseous phases in this environment. This solver uses perfect gas and stiffened gas models for equation of state, with the ability to easily add other models as desired. Additionally a comparison of a Riemann solver versus an AUSM+up scheme is conducted, showing improvement with the later in the solution of multiphase flows. This solver successfully reproduces shock tube cases with the expected accuracy, as well as simulating two-dimensional shear and gravity-driven flows. Results also show that the code is able to utilize a Stratified Flow model to evaluate shear flow without the need for interface reconstruction or gradient calculations. Finally, it is shown that the solver has near-ideal scaling under strong scaling tests as well as good performance in static scaling, giving improved performance over current options and implying future advancement of high-performance computing efficiency for multiphase flow solvers.

97 MATHEMATICS AND COMPUTING↗

Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gas-stirred Ladles

In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.

36 MATERIALS SCIENCE↗

Flow Loop Study of ECT-Based Volume Fraction Monitoring in Oil–Water Two-Phase Flows

Measurement of phase volume fractions in water-containing multiphase flows is necessary for the optimization of a host of industrial flow processes. Many water-containing multiphase flows can be classified as either water-dispersed or water-continuous mixtures. A recently developed approach based on Hanai’s mixture formula and utilizing electrical capacitance tomography (ECT) sensors have shown good potential for obtaining water volume fraction estimates in two-phase water-containing flows with different water salinity levels. However, the proposed approach was investigated via controlled experiments restricted to static configurations while, in practice, multiphase flows can be dynamic and unpredictable. In this work, we perform a flow loop study of the proposed ECT-based method for volume fraction estimation in oil–water two-phase flows. Here, we evaluate the performance of the proposed method in both water-dispersed and water-continuous flow regimes by employing different types of capacitive sensors in cylindrical arrangements and parallel-plate rectangular arrangements.

02 PETROLEUM↗

Experimental Investigation of Buoyant Flow in Realistic Bedforms With Heterogeneous Wettability

Submeter-scale geologic heterogeneity greatly affects CO 2 plume migration and retention. In this work, we present meter-scale laboratory experiments that can capture the impact of realistic submeter-scale geologic heterogeneity on multiphase flow and trapping. We produce realistic sedimentary formations consisting of ripple deposits with varying grain size contrast and wettability in a meter-scale slab chamber. Then, we conduct multiphase flow experiments with analog fluids through these structures and measure the saturation patterns, capillary heterogeneity trapping (CHT), and overall trapping performance. When we alter the ripple bedform architecture, variations in trapped saturation and CHT (10–20%) increment are exhibited. Similar growth in trapping performance is also observed when grain size contrast increases. Finally, wettability changes (water- to oil-wet) can increase nonwetting saturation and CHT up to 5% and 10–20%, respectively. These results emphasize the importance of correctly characterizing the impact of small-scale heterogeneities and wettability changes. We believe this is the first time that multiphase flow experiments were conducted in meter-scale domains with realistic ripple bedforms and heterogeneous wettability to investigate plume migration and trapping.

58 GEOSCIENCES↗

Theoretical Review of the MFIX Fluid and Two-Fluid Models

MFIX (Multiphase Flow with Interphase eXchanges) is a general purpose code that can be used for describing the hydrodynamics, chemical reactions, and heat transfer of dense or dilute multiphase fluid flows. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the defined system. This report provides an overview of MFIX’s expressions for single phase flow and continuous dispersed multiphase flow (i.e., the two-fluid model). In addition to the two fluid model (MFIX-TFM), MFIX contains a discrete element model (MFIX-DEM) and a multi-phase particle in cell model (MFIX-PIC) that are not reviewed within this document.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Lattice Boltzmann Method for Predicting Porous Transport Layer Performance During Electrolysis

Electrolysis, the splitting of water into oxygen and hydrogen using electricity, is a sustainable way to produce green hydrogen for energy storage. In polymer electrolyte membrane (PEM) water electrolysis, water is brought into contact with charged catalyst layers and electrochemically separated into oxygen and hydrogen. The hydrogen product formed at the cathode is carried through the catalyst layer for eventual collection, while the oxygen by-product formed at the anode is removed from the surface via a multiphase interaction with circulating water and a solid porous transport layer (PTL). The design of this PTL aids in the detachment and advection of the oxygen by-product and thereby plays a role in the overall efficacy of the catalyst. In this presentation, we present our initial results modeling this multiphase system using a single-component, multiphase lattice Boltzmann method. We use the Shan-Chen model describing inter-particle forces to capture both the cohesion of the water (liquid) and oxygen (gas) phases and their interaction with the PTL (solid) (Shan and Chen, 1993). We use a Carnahan-Starling equation of state to model the effective density governing these inter-particle interactions which allows us to model this relatively high density ratio system (Carnahan and Starling, 1969). With these simulations, we show that the geometry and heterogeneity of the PTL geometry plays a large role in its ability to move oxygen away from the catalyst layer and the resulting bubble structures that are formed within the PTL. The current work demonstrates these effects using synthesized PTL geometries and 2D physics, which will be extended to experimentally-imaged PTL sections and 3D algorithms in the near future.

Boltzmann↗